16TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS 1 - PDF document

16TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS 1
Abstract This paper presents the analysis of a honeycomb core sandwich composite subject to a low velocity impact, resulting in barely visible impact damage (BVID). The damage to the composite structure and the subsequent reduction in load carrying capability are predicted and compared to experiment using ABAQUS. An anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials is detailed. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes -- fiber tension, fiber compression, matrix tension, and matrix compression -- are considered and modeled separately. The results of the impact simulation are used as initial conditions for the compression after impact (CAI) simulations to determine loss of structural strength. 1 Introduction In the continual effort to develop products with better performance at lower cost and weight, the use of composite materials in the aerospace industry is increasing at a significant rate. These materials offer many benefits over traditional metallic designs, including high strength-to-weight ratio, part count reduction and improved corrosion resistance. Today’s exploitation of the benefits of composite materials requires that new methods, and often new technologies, be developed for analyzing and determining margins of safety for these components. Composites have very different failure mechanisms than traditional metals; therefore the analysis processes that have been used in the past are no longer applicable. New simulation technologies need to be developed to accurately represent composite components and to realistically simulate their failure modes. A particularly challenging design problem for composite materials in the aerospace industry is barely visible impact damage (BVID). Even low speed impact on composite structures can lead to a significant decrease in load carrying capability, with little or no visible evidence of damage. This paper presents and discusses the development and implementation of a progressive damage and failure model for unidirectional fiber carbon composites based on the Hashin damage criteria, and presents an example of its use for predicting BVID in aerospace structures. 2 Composite Damage Model To capture the effects of progressive damage and failure on laminated composite structures, failure modes in both the fiber and matrix material must be considered. The model developed here considers anisotropic damage through four separate modes: fiber failure in tension and compression, as well as matrix failure in tension and compression. The complete details of the composite damage model can be found in Lapczyk and Hurtado [1]. An overview of the approach used is discussed here. The effect of damage in the material is taken into account by reducing the stiffness as originally proposed by Kachanov [2]. In the treatment used here, the model suggested by Matzenmiller [3] to compute the degraded stiffness matrix is used. The relation between effective stress and nominal stress is assumed to take the form where M is the damage operator, which has the diagonal form = (1) ANALYSIS OF BARELY VISIBLE IMPACT DAMAGE FOR AEROSPACE STRUCTURES Sandor Becz, Juan Hurtado, Ireneusz Lapczyk ABAQUS, Inc. Keywords: composite, damage, failure, impact, BVID, unidirectional, fiber SANDOR BECZ, Hurtado, Lapczyk where , , are damage variables for the fiber, matrix and shear failure modes, respectively. Using this expression it is possible to develop a damaged compliance matrix of the form and the corresponding stiffness matrix where d = (1 - d)(1 - d), D= 1-d1221, and , and 12 are the undamaged moduli. The rate of energy dissipation when the material is damaged is given by In this equation, Yft, Yfc, Ymt, Ymc are the thermodynamic forces corresponding to the different failure modes, which are computed from the relation and the Gibbs free energy, which for this model takes the form It can be easily verified that the energy dissipated is a monotonically increasing quantity. The damage initiation is calculated based on the work of Hashin (Hashin and Rotem [4], Hashin [5]) and have the following general forms: Fiber tension: Fiber compression: Matrix tension: Matrix compression: Mesh dependency is a common problem when modeling materials with stiffness degradation. The model used here includes the crack band model of Bazant and Oh [6] in which fracture is modeled as a (2) () () () 121221 (3) ( ) ()()1221 (4) ftftftft




(5) iidGY¶ ¶ (6) () mcmtfcft121222111222221111(7) 1211(8) 11II(9) 1222III(10) 122222IV (11) 3 ANALYSIS OF BARELY VISIBLE IMPACT DAMAGE FOR AEROSPACE STRUCTURES band of parallel densely distributed microcracks (a smeared crack band). In the model, the fracture energies of the material must be specified for each failure mode. A discussion of how the fracture energies can be estimated is provided in Maimi et al. [7]. 3 Application to a BVID Problem With a damage representation in hand, an application of its use for predicting barely visible impact damage is considered. Details of the analysis process are provided in the following section. 3.1 Model Setup The composite modeled for the BVID simulation was a honeycomb core sandwich material with unidirectional carbon fiber facesheets. The analysis used the same geometry as the test specimens of McGowan and Ambur [8]. The overall dimensions of these specimens are provided in Figure 1. Each facesheet of the composite specimen consisted of 38 plies of AS4/8552 graphite-epoxy pre-impregnated tow material with a layup as follows: ±45/0/+45/90/-45/0/-45/90/+45/0/-45/90/0/ +45/0/+45/0/-45/0/+45/0/90/-45/0/+45/90/-45/ 0/-45/90/+45/0/-+45] The material properties used in the analysis for the composite facesheets were taken from the values provided in [2] and are listed in Table 1. Table 1: Material properties used for analysis of AS4/8552 11GPa 22Gpa 12GPa 12Ply thickness 122.7 9.38 5.28 0.32 0.19 mm The impact energy for the drop simulation was set to 81.3 J by specifying an initial velocity of 3.9 m/s with a drop mass weight of 5.36 kgs. The impactor was modeled as a sphere of 25.4 mm. diameter. The facesheets were modeled using continuum shell elements (SC8R) which are defined using a solid element topology but use a shell element formulation. The shell section was defined using the composite material definition capability available in ABAQUS. The inputs to the definition include the number of layers, material and fiber orientation for each layer, and individual layer thicknesses. The honeycomb core material was meshed using reduced integration continuum solid elements (C3D8R) and defined using an orthotropic material definition. Figure 1: Geometry used for BVID simulation (from [8]) The composite material was meshed using a structured hexahedral topology, with refinement toward the center of the section in the area of impact. A view of the mesh applied to the geometry is presented in Figure 2. The spherical impactor was meshed with tetrahedral elements and was assumed to be rigid. During the impact simulation, the edges of the composite structure were fixed in all degrees of freedom. During the subsequent compression simulation, one end of the specimen was freed to allow a specified displacement to be applied, while the sides of the structure were unconstrained. 3.1 Analysis Process To first capture the effects of impact in the composite material, a drop simulation is performed using ABAQUS/Explicit. The low speed impact does not impart enough energy to cause material failure; however the progressive damage model SANDOR BECZ, Hurtado, Lapczyk (a) (b) Figure 2: Hexahedral mesh used for sandwich composite structure; (a) top view, (b) cross section tracks the approach of the material to the initiation of damage, which accumulates monotonically. The subsequent CAI simulation will continue to move the material state toward the initiation of damage, and eventually damage (and subsequently failure) will occur. After the impact simulation is completed, the CAI simulation utilizes the damage state at the end of the dynamic event as the initial condition in ABAQUS/Standard by importing the material state. The compression simulation is continued until convergence is no longer possible. This is considered the failure condition of the specimen. 5 Results 5.1 Impact Results The primary results of interest from the initial impact event are the location and amount of accumulated damage, or progress toward the initiation of damage that has occurred. In addition, it is instructive to determine the mode of failure which has been most significantly affected. Figure 3 present contours of the progress toward the start of damage for the matrix material in the top layer of the face sheet upon which the impactor strikes. The peak value can be seen to be 0.988, or very close to the point at which the material will begin to experience damage. Of significant importance to note is that progress toward the initiation of damage occurs not only locally in the area of impact, but also at the bottom faces of both face sheets due to stress wave propagation and reflection. This can be seen by the plots in Figures 4 and 5. Figure 3: Contours of progression toward initiationof matrix compression damage in the top layer of the top face sheet 5 ANALYSIS OF BARELY VISIBLE IMPACT DAMAGE FOR AEROSPACE STRUCTURES Figure 4: Contours of progress toward damage for the bottom layer of the top face sheet Figure 4 presents contours of the approach to compressive matrix damage for the bottom ply of the face sheet which has been impacted by the sphere. Although the progress variable is much lower than for the ply which was directly impacted (0.350 vs. 0.988), the bottom ply will fail earlier than an undamaged ply when a subsequent additional load is applied. In addition, Figure 5 presents the same variable for the bottom ply of the face sheet on the opposite side of the honeycomb core. Even here some progress toward damage has occurred. These results clearly point out how troublesome barely visible impact damage to composites can be. Looking now at other potential failure modes, we find other surprising results when considering tensile matrix and fiber progression to damage on Figure 5: Contours of progress toward damage for the bottom layer of the bottom face sheet the bottom ply of the top facesheet. These contours are shown in Figures 6 and 7, respectively. Here we find that due to reflection of the initial compressive stress wave off of the facesheet/honeycomb interface, a tensile wave produces large enough stress such that damage has been initiated in the tensile matrix mode, and is nearly 70% of the way toward activating the tensile fiber damage mode. We again see how important it is to understand the full effects of even low speed impact on composite structures. 5.2 Compression After Impact Results The most important aspect of the prediction of barely visible impact damage is the assessment of the reduction of load carrying capability of the affected material. The damage model described SANDOR BECZ, Hurtado, Lapczyk Figure 6: Contours of progression toward matrix tensile damage in the bottom ply of the top facesheet previously predicts a monotonically increasing progression toward the start of damage, and then debits the material stiffness as damage increases. During the CAI simulation, failure modes will continue to advance from the end state of the impact simulation. However, the progression of these modes will now be dictated by those that are most strongly effected by the compressive load. In general the most sensitive mechanism will be compressive matrix failure. Figure 8 presents contours of matrix damage in the composite material as the structure nears failure. The similarity to the final damaged state of the actual test specimen from [8], shown in Figure 9, is evident. Finally, Figure 10 presents the load-displacement curve of the simulated structure for both the undamaged and damaged specimens. The Figure 7: Contours of progression toward fiber compressive damage in the bottom ply of the top facesheet values for the undamaged panel are taken from [8]. The predicted reduction in load carrying capability is approximately 20%, which is much less than the 45% reduction seen in the test results. Potential causes for the difference include the neglect of additional physical mechanisms which will clearly contribute to the response, including delamination and large scale buckling. 6 Conclusions The increased use of composite materials for primary aerospace structures such as wings and control surfaces makes it critical to understand the effects of non-visible damage to these components. This paper has presented a progressive damage and failure model for unidirectional composite materials that is appropriate for structures which exhibit primarily elastic behavior up to failure. The model 7 ANALYSIS OF BARELY VISIBLE IMPACT DAMAGE FOR AEROSPACE STRUCTURES Figure 8: Contours of matrix damage near failure of the honeycomb sandwich composite structure Figure 9: Final damaged state of the composite test specimen (from [8]) presented considers both compressive and tensile failure for both the fiber and matrix material. Using this model, an analysis was performed to predict the reduction in load carrying capability of a honeycomb sandwich unidirectional fiber facesheet structure. An initial impact simulation was performed in ABAQUS/Explicit which provided the initial conditions for a subsequent compression after impact simulation in ABAQUS/Standard. The results of the simulation showed that damage begins to accumulate not only in the local region of impact, but also at the honeycomb/facesheet interface due to stress wave propagation and reflection. An overall load carrying capability reduction of approximately 20% was predicted, which underestimates the reduction found in an equivalent test specimen. References [1]Lapczyk E. and Hurtado J. “Progressive damage modeling in fiber reinforced materials”. Journal of Composites, Part A, JCOMA-06-183, in press. [2] Kachanov LM. “On the time to failure under creep conditions”. Izv. AN SSSR, Otd. Tekhn., 1958, 8:26-31. [3]Matzenmiller A, Lubliner J, Taylor, RL. “A constitutive model for anisotropic damage in fiber-composites”. Mechanics of Materials, 1995, 20:125-152. [4]Hashin Z, Rotem A. “A fatigue failure criterion for fiber-reinforced materials”, Journal of Composite Materials. 1973, 7:448 [5]Hashin Z. “Failure criteria for unidirectional fiber composites”. Journal of Applied Mechanics, 1980, 47:329-334. [6]Baant ZP, Oh BH. Crack Band Theory for Fracture of Concrete. Mater. Struct., 1983, 16:155–177. [7]Maimi P, Camanho PP, Mayugo J , Dávila CG. “A thermodynamically consistent damage model for advanced composites”. Tech. Rep. NASA/TM-2006-214282, 2006.[8]MCGowan, D.M. and Ambur, D.R., “Damage Tolerance Characteristics of Composite Fuselage Sandwich Structures With Thick Facesheets”, NASA TM-110303 SANDOR BECZ, Hurtado, Lapczyk 20,00040,00060,00080,000100,000120,000140,000160,000180,000200,0000.000.020.040.060.080.100.12Displacement (in)Load (lb) Undamaged Damaged Figure 10: Result of ABAQUS simulation load-displacement curve for damaged and undamaged composite material specimen during compression after impact